Cut the cooked ham into strips. Finely chop the garlic. Heat a little olive oil with a little butter in a pan and lightly fry the ham. Add the garlic and fry a little more.
Finely chop the parsley and coarsely grate the Parmigiano Reggiano. Deglaze with the vegetable stock, ham and garlic and bring to the boil. Add the cream and milk and continue cooking. Add a little grated Parmigiano Reggiano and let melt while stirring. Salt lightly and pepper strongly. Reduce to the desired consistency and season with chopped parsley, salt, pepper and Parmigiano Reggiano.